# Handphone Paradox

You showed your friend your handphone and your friend shows you his.

Both of you start to compare and you claim that your handphone is cheaper than his and he claims that his handphone is cheaper than yours.

Hence you start a bet – after you check the actual prices, the one whose handphone is more expensive will give his handphone to the one whose handphone is cheaper.

You reckon since you will either lose your cheaper handphone or gain a more expensive handphone, it must make sense to bet.

Does this make sense?

Solution:

No! Your friend has the same mentality too – that he will either lose his cheaper handphone or gain a more expensive handphone, and thus enters the bet.

But both of you cannot win, so let us examine the probabilities.

Assuming that your handphones cost either $10 or $20 for easy calculations.

Case 1:

Your handphone – $10

Friend’s handphone – $20

Your friend gives to you his $20 handphone.

Case 2:

Your handphone – $20

Friend’s handphone – $10

You give your friend your $20 handphone.

Expected value = $20 – $20 = $0.

No one will stand to gain from this bet!